Abstract

Continuum robot manipulators present challenges for controller design due to the complexity of their infinite-dimensional dynamics. This paper develops a practical dynamics-based approach to synthesizing state feedback controllers for a soft continuum robot arm composed of segments with local sensing, actuation, and control capabilities. Each segment communicates its states to its two adjacent neighboring segments, requiring a tridiagonal feedback matrix for decentralized controller implementation. A semi-discrete numerical approximation of the Euler-Bernoulli beam equation is used to represent the robot arm dynamics. Formulated in state space representation, this numerical approximation is used to define an H-{\infty} optimal control problem in terms of a Bilinear Matrix Inequality. We develop three iterative algorithms that solve this problem by computing the tridiagonal feedback matrix which minimizes the H-{\infty} norm of the map from disturbances to regulated outputs. We confirm through simulations that all three controllers successfully dampen the free vibrations of a cantilever beam that are induced by an initial sinusoidal displacement, and we compare the controllers' performance.

title = "Decentralized Control of Distributed Actuation in a Segmented Soft Robot Arm",

abstract = "Continuum robot manipulators present challenges for controller design due to the complexity of their infinite-dimensional dynamics. This paper develops a practical dynamics-based approach to synthesizing state feedback controllers for a soft continuum robot arm composed of segments with local sensing, actuation, and control capabilities. Each segment communicates its states to its two adjacent neighboring segments, requiring a tridiagonal feedback matrix for decentralized controller implementation. A semi-discrete numerical approximation of the Euler-Bernoulli beam equation is used to represent the robot arm dynamics. Formulated in state space representation, this numerical approximation is used to define an H-{\infty} optimal control problem in terms of a Bilinear Matrix Inequality. We develop three iterative algorithms that solve this problem by computing the tridiagonal feedback matrix which minimizes the H-{\infty} norm of the map from disturbances to regulated outputs. We confirm through simulations that all three controllers successfully dampen the free vibrations of a cantilever beam that are induced by an initial sinusoidal displacement, and we compare the controllers' performance.",

author = "Azadeh Doroudchi and Sachin Shivakumar and Fisher, {Rebecca E.} and Hamidreza Marvi and Daniel Aukes and Ximin He and Spring Berman and Matthew Peet",

year = "2019",

month = "1",

day = "18",

doi = "10.1109/CDC.2018.8619036",

language = "English (US)",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "7002--7009",

booktitle = "2018 IEEE Conference on Decision and Control, CDC 2018",

}

TY - GEN

T1 - Decentralized Control of Distributed Actuation in a Segmented Soft Robot Arm

AU - Doroudchi, Azadeh

AU - Shivakumar, Sachin

AU - Fisher, Rebecca E.

AU - Marvi, Hamidreza

AU - Aukes, Daniel

AU - He, Ximin

AU - Berman, Spring

AU - Peet, Matthew

PY - 2019/1/18

Y1 - 2019/1/18

N2 - Continuum robot manipulators present challenges for controller design due to the complexity of their infinite-dimensional dynamics. This paper develops a practical dynamics-based approach to synthesizing state feedback controllers for a soft continuum robot arm composed of segments with local sensing, actuation, and control capabilities. Each segment communicates its states to its two adjacent neighboring segments, requiring a tridiagonal feedback matrix for decentralized controller implementation. A semi-discrete numerical approximation of the Euler-Bernoulli beam equation is used to represent the robot arm dynamics. Formulated in state space representation, this numerical approximation is used to define an H-{\infty} optimal control problem in terms of a Bilinear Matrix Inequality. We develop three iterative algorithms that solve this problem by computing the tridiagonal feedback matrix which minimizes the H-{\infty} norm of the map from disturbances to regulated outputs. We confirm through simulations that all three controllers successfully dampen the free vibrations of a cantilever beam that are induced by an initial sinusoidal displacement, and we compare the controllers' performance.

AB - Continuum robot manipulators present challenges for controller design due to the complexity of their infinite-dimensional dynamics. This paper develops a practical dynamics-based approach to synthesizing state feedback controllers for a soft continuum robot arm composed of segments with local sensing, actuation, and control capabilities. Each segment communicates its states to its two adjacent neighboring segments, requiring a tridiagonal feedback matrix for decentralized controller implementation. A semi-discrete numerical approximation of the Euler-Bernoulli beam equation is used to represent the robot arm dynamics. Formulated in state space representation, this numerical approximation is used to define an H-{\infty} optimal control problem in terms of a Bilinear Matrix Inequality. We develop three iterative algorithms that solve this problem by computing the tridiagonal feedback matrix which minimizes the H-{\infty} norm of the map from disturbances to regulated outputs. We confirm through simulations that all three controllers successfully dampen the free vibrations of a cantilever beam that are induced by an initial sinusoidal displacement, and we compare the controllers' performance.